Non‐linear bifurcation method to determine the boost converter switching frequency

Abstract

Prior to the design of the feedback system for a boost converter, a suitable switching frequency for the transistor has to be determined. A non-linear method for determining this frequency via an experimental open-loop converter model is studied. Utilising the open-loop model as an investigative tool, two non-linear distinct resonant frequencies have been found to be a source of chaos. This condition for chaos holds when the boost diode's reverse-recovery time, its non-linear capacitance, as well as the inductance are the combined parameters within these frequencies. When the switching frequency is synchronised with these frequencies, ultra-harmonics, period-doublings and sudden transitions to chaos occur for various switching frequency ranges. The dependence equations of our theoretical model that incorporate these resonant frequencies predict the unstable frequency regions. The authors’ numerical method utilises a bifurcation peak-to-peak analysis that detects the waveform periodicity of certain voltage variables. Highly unstable behaviour of the converter is reported both in simulation and in the laboratory. The periodic and non-periodic regions are confirmed by the corresponding computations of the Lyapunov exponent, Poincare sections, frequency spectra and bifurcation diagrams.